Sphere of Equivalence—A Novel Target Volume Concept for Intraoperative Radiotherapy Using Low-Energy X Rays

Abstract

Accelerated partial breast radiotherapy with low-energy photons from a miniature X-ray machine is undergoing a randomized clinical trial (Targeted Intra-operative Radiation Therapy [TARGIT]) in a selected subgroup of patients treated with breast-conserving surgery. The steep radial dose gradient implies reduced tumor cell control with increasing depth in the tumor bed. The purpose was to compare the expected risk of local recurrence in this nonuniform radiation field with that after conventional external beam radiotherapy. The relative biologic effectiveness of low-energy photons was modeled using the linear-quadratic formalism including repair of sublethal lesions during protracted irradiation. Doses of 50-kV X-rays (Intrabeam) were converted to equivalent fractionated doses, EQD2, as function of depth in the tumor bed. The probability of local control was estimated using a logistic dose-response relationship fitted to clinical data from fractionated radiotherapy. The model calculations show that, for a cohort of patients, the increase in local control in the high-dose region near the applicator partly compensates the reduction of local control at greater distances. Thus a "sphere of equivalence" exists within which the risk of recurrence is equal to that after external fractionated radiotherapy. The spatial distribution of recurrences inside this sphere will be different from that after conventional radiotherapy. A novel target volume concept is presented here. The incidence of recurrences arising in the tumor bed around the excised tumor will test the validity of this concept and the efficacy of the treatment. Recurrences elsewhere will have implications for the rationale of TARGIT.